Find intervals on the fretboard fast: 3x3 Box Technique
"They thought they were identifying a set of behaviours, but yeah, they just wanted to have an answer." - Chester Brown

Intervals are more important than the notes themselves.
The way we can build chords and create melodies is by superimposing notes with specific intervals that carry weight or emotion.
In order to be able to come up with those on the fly, especially while improvising, you need to be able to identify the intervals on the fretboard. The faster, the better, of course.
In this lesson, I'll show you my method for finding out the intervals quickly on the fretboard.
Don't forget to check the infographic at the bottom!
If you don't want to read, you can watch the video lesson.
Unless you are using a very unorthodox tuning on your guitar, most of the intervals are placed very closely together on the fretboard. From now on, I'll assume a standard EADGBE tuning, although this will also work for any drop tuning too.
Take a look at this figure:

See the area that's enclosed in the rounded rectangle? It's a 3-fret by 3-string square.
We'll find that most intervals are within that figure. This is why I call this technique the "3x3 Box Technique".
Let's pick any note on the 6th string as a starting note, let's say the 5th fret, which corresponds to an A note. The most important and straightforward intervals are the 5th (E) and the 8th (octave, A), which can be found within the figure:

Of course, the numbers in this case mean the intervals, not fingers!
These notes tend are usually the strongest notes you can play on top of most chords, since they are the notes that appear in almost all chords. Playing them will always sound right.
In my opinion, these notes are the easiest to find starting from the root.
There are more intervals to be found there as well: 2nd (B), 4th (D), and 7th (Ab).

By focusing on this single block figure, it's much easier to identify the intervals all over the fretboard, starting from a root note.
There are two more intervals which are very important that we cannot find in this figure technically. These are the major and minor 3rd (C# and C respectively), which lie just outside the figure.

These are the only two extra intervals you'll have to refer to.
This are the complete intervals:

The interesting thing about this pattern is that it can be moved anywhere on the fretboard, with the root notes in any string. You can even use it backwards, that is consider the octave note as the root note and find the same intervals.
Here's how it looks on a root note on the 5th string:

Now, I know I said that the figure holds anywhere on the fretboard, however, this is not entirely true, due to the tuning of the 2nd string. I'll show you.
Let's consider a root note on the 4th string, 5th fret (G), like so:

If we followed the same diagram we saw before, we would say that the octave note should be in the 7th fret, 2nd string. However, that note is not a G, but an F#. Why is that?
Remember that the standard tuning is done with each string being tuned a 4th interval than the one above (E to A, A to D, D to G), until when we get to the 2nd string, which is tuned a 3rd above the 3rd string. The 2nd string is tuned to a B whereas the 3rd string is a G. This means that each note on the 2nd string is one semitone (one fret) lagged in comparison to the other strings.
This is a simple fix, though. We can still use the same figure, but we have to shift all the notes on the 2nd string one fret forward.
To remember this, you can pretend there is a waterline betwen the 3rd and 2nd strings. Remember what happens when you put a pencil inside a glass with water?

This is what's called as light refraction.
Yeah, I know, we're not going to get on to a physics class, but notice how the pencil seems to be fractured and moved to a side?
Well, let's consider that the pencil is on the fretboard and that there is a waterline between the 3rd and 2nd strings.

See how the square is warped, the same way as the pencil is warped, accross our hypothetical waterline?
By looking at this in this way, we can then use the same figure we had seen before, but affected by the diffraction of the water, like so:

And, of course, a similar thing applies when we consider the root note on the 3rd string, like so:

So...we've already seen how to find intervals quickly starting from a root note, but...what can we use this for?
Well, there are two main uses that are very straightforward:
Identify intervals in chords.
Add dimension while improvising.
So, the first use is pretty straightforward. If you see any chord shape you don't recognize, you will be able to quickly find out the intervals just by looking at the positions of each note on the fretboard starting from the root note of the chord.
When improvising, you usually play either a melody or a run that's already ingrained in your mind. I like to start on the root note of the chord I'm playing over, and start moving accross the different intervals I want to emphasize. It doesn't matter if you know in which key you are playing, you can always visually identify the interval you want to play to create a desired effect.
Don't worry, we'll see more on this later.
You can leave any comments below.
Here is the infographic.
